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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.stat.correlation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.MathUnsupportedOperationException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.linear.MatrixUtils;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.linear.RealMatrix;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    /**<a name="line.25"></a>
<FONT color="green">026</FONT>     * Covariance implementation that does not require input data to be<a name="line.26"></a>
<FONT color="green">027</FONT>     * stored in memory. The size of the covariance matrix is specified in the<a name="line.27"></a>
<FONT color="green">028</FONT>     * constructor. Specific elements of the matrix are incrementally updated with<a name="line.28"></a>
<FONT color="green">029</FONT>     * calls to incrementRow() or increment Covariance().<a name="line.29"></a>
<FONT color="green">030</FONT>     *<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;This class is based on a paper written by Philippe P&amp;eacute;bay:<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;a href="http://prod.sandia.gov/techlib/access-control.cgi/2008/086212.pdf"&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * Formulas for Robust, One-Pass Parallel Computation of Covariances and<a name="line.33"></a>
<FONT color="green">034</FONT>     * Arbitrary-Order Statistical Moments&lt;/a&gt;, 2008, Technical Report SAND2008-6212,<a name="line.34"></a>
<FONT color="green">035</FONT>     * Sandia National Laboratories.&lt;/p&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     *<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;Note: the underlying covariance matrix is symmetric, thus only the<a name="line.37"></a>
<FONT color="green">038</FONT>     * upper triangular part of the matrix is stored and updated each increment.&lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     *<a name="line.39"></a>
<FONT color="green">040</FONT>     * @version $Id: StorelessCovariance.java 1410238 2012-11-16 07:58:49Z luc $<a name="line.40"></a>
<FONT color="green">041</FONT>     * @since 3.0<a name="line.41"></a>
<FONT color="green">042</FONT>     */<a name="line.42"></a>
<FONT color="green">043</FONT>    public class StorelessCovariance extends Covariance {<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>        /** the square covariance matrix (upper triangular part) */<a name="line.45"></a>
<FONT color="green">046</FONT>        private StorelessBivariateCovariance[] covMatrix;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /** dimension of the square covariance matrix */<a name="line.48"></a>
<FONT color="green">049</FONT>        private int dimension;<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>        /**<a name="line.51"></a>
<FONT color="green">052</FONT>         * Create a bias corrected covariance matrix with a given dimension.<a name="line.52"></a>
<FONT color="green">053</FONT>         *<a name="line.53"></a>
<FONT color="green">054</FONT>         * @param dim the dimension of the square covariance matrix<a name="line.54"></a>
<FONT color="green">055</FONT>         */<a name="line.55"></a>
<FONT color="green">056</FONT>        public StorelessCovariance(final int dim) {<a name="line.56"></a>
<FONT color="green">057</FONT>            this(dim, true);<a name="line.57"></a>
<FONT color="green">058</FONT>        }<a name="line.58"></a>
<FONT color="green">059</FONT>    <a name="line.59"></a>
<FONT color="green">060</FONT>        /**<a name="line.60"></a>
<FONT color="green">061</FONT>         * Create a covariance matrix with a given number of rows and columns and the<a name="line.61"></a>
<FONT color="green">062</FONT>         * indicated bias correction.<a name="line.62"></a>
<FONT color="green">063</FONT>         *<a name="line.63"></a>
<FONT color="green">064</FONT>         * @param dim the dimension of the covariance matrix<a name="line.64"></a>
<FONT color="green">065</FONT>         * @param biasCorrected if &lt;code&gt;true&lt;/code&gt; the covariance estimate is corrected<a name="line.65"></a>
<FONT color="green">066</FONT>         * for bias, i.e. n-1 in the denominator, otherwise there is no bias correction,<a name="line.66"></a>
<FONT color="green">067</FONT>         * i.e. n in the denominator.<a name="line.67"></a>
<FONT color="green">068</FONT>         */<a name="line.68"></a>
<FONT color="green">069</FONT>        public StorelessCovariance(final int dim, final boolean biasCorrected) {<a name="line.69"></a>
<FONT color="green">070</FONT>            dimension = dim;<a name="line.70"></a>
<FONT color="green">071</FONT>            covMatrix = new StorelessBivariateCovariance[dimension * (dimension + 1) / 2];<a name="line.71"></a>
<FONT color="green">072</FONT>            initializeMatrix(biasCorrected);<a name="line.72"></a>
<FONT color="green">073</FONT>        }<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>        /**<a name="line.75"></a>
<FONT color="green">076</FONT>         * Initialize the internal two-dimensional array of<a name="line.76"></a>
<FONT color="green">077</FONT>         * {@link StorelessBivariateCovariance} instances.<a name="line.77"></a>
<FONT color="green">078</FONT>         *<a name="line.78"></a>
<FONT color="green">079</FONT>         * @param biasCorrected if the covariance estimate shall be corrected for bias<a name="line.79"></a>
<FONT color="green">080</FONT>         */<a name="line.80"></a>
<FONT color="green">081</FONT>        private void initializeMatrix(final boolean biasCorrected) {<a name="line.81"></a>
<FONT color="green">082</FONT>            for(int i = 0; i &lt; dimension; i++){<a name="line.82"></a>
<FONT color="green">083</FONT>                for(int j = 0; j &lt; dimension; j++){<a name="line.83"></a>
<FONT color="green">084</FONT>                    setElement(i, j, new StorelessBivariateCovariance(biasCorrected));<a name="line.84"></a>
<FONT color="green">085</FONT>                }<a name="line.85"></a>
<FONT color="green">086</FONT>            }<a name="line.86"></a>
<FONT color="green">087</FONT>        }<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>        /**<a name="line.89"></a>
<FONT color="green">090</FONT>         * Returns the index (i, j) translated into the one-dimensional<a name="line.90"></a>
<FONT color="green">091</FONT>         * array used to store the upper triangular part of the symmetric<a name="line.91"></a>
<FONT color="green">092</FONT>         * covariance matrix.<a name="line.92"></a>
<FONT color="green">093</FONT>         *<a name="line.93"></a>
<FONT color="green">094</FONT>         * @param i the row index<a name="line.94"></a>
<FONT color="green">095</FONT>         * @param j the column index<a name="line.95"></a>
<FONT color="green">096</FONT>         * @return the corresponding index in the matrix array<a name="line.96"></a>
<FONT color="green">097</FONT>         */<a name="line.97"></a>
<FONT color="green">098</FONT>        private int indexOf(final int i, final int j) {<a name="line.98"></a>
<FONT color="green">099</FONT>            return j &lt; i ? i * (i + 1) / 2 + j : j * (j + 1) / 2 + i;<a name="line.99"></a>
<FONT color="green">100</FONT>        }<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        /**<a name="line.102"></a>
<FONT color="green">103</FONT>         * Gets the element at index (i, j) from the covariance matrix<a name="line.103"></a>
<FONT color="green">104</FONT>         * @param i the row index<a name="line.104"></a>
<FONT color="green">105</FONT>         * @param j the column index<a name="line.105"></a>
<FONT color="green">106</FONT>         * @return the {@link StorelessBivariateCovariance} element at the given index<a name="line.106"></a>
<FONT color="green">107</FONT>         */<a name="line.107"></a>
<FONT color="green">108</FONT>        private StorelessBivariateCovariance getElement(final int i, final int j) {<a name="line.108"></a>
<FONT color="green">109</FONT>            return covMatrix[indexOf(i, j)];<a name="line.109"></a>
<FONT color="green">110</FONT>        }<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>        /**<a name="line.112"></a>
<FONT color="green">113</FONT>         * Sets the covariance element at index (i, j) in the covariance matrix<a name="line.113"></a>
<FONT color="green">114</FONT>         * @param i the row index<a name="line.114"></a>
<FONT color="green">115</FONT>         * @param j the column index<a name="line.115"></a>
<FONT color="green">116</FONT>         * @param cov the {@link StorelessBivariateCovariance} element to be set<a name="line.116"></a>
<FONT color="green">117</FONT>         */<a name="line.117"></a>
<FONT color="green">118</FONT>        private void setElement(final int i, final int j,<a name="line.118"></a>
<FONT color="green">119</FONT>                                final StorelessBivariateCovariance cov) {<a name="line.119"></a>
<FONT color="green">120</FONT>            covMatrix[indexOf(i, j)] = cov;<a name="line.120"></a>
<FONT color="green">121</FONT>        }<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>        /**<a name="line.123"></a>
<FONT color="green">124</FONT>         * Get the covariance for an individual element of the covariance matrix.<a name="line.124"></a>
<FONT color="green">125</FONT>         *<a name="line.125"></a>
<FONT color="green">126</FONT>         * @param xIndex row index in the covariance matrix<a name="line.126"></a>
<FONT color="green">127</FONT>         * @param yIndex column index in the covariance matrix<a name="line.127"></a>
<FONT color="green">128</FONT>         * @return the covariance of the given element<a name="line.128"></a>
<FONT color="green">129</FONT>         * @throws NumberIsTooSmallException if the number of observations<a name="line.129"></a>
<FONT color="green">130</FONT>         * in the cell is &amp;lt; 2<a name="line.130"></a>
<FONT color="green">131</FONT>         */<a name="line.131"></a>
<FONT color="green">132</FONT>        public double getCovariance(final int xIndex,<a name="line.132"></a>
<FONT color="green">133</FONT>                                    final int yIndex)<a name="line.133"></a>
<FONT color="green">134</FONT>            throws NumberIsTooSmallException {<a name="line.134"></a>
<FONT color="green">135</FONT>    <a name="line.135"></a>
<FONT color="green">136</FONT>            return getElement(xIndex, yIndex).getResult();<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>        }<a name="line.138"></a>
<FONT color="green">139</FONT>    <a name="line.139"></a>
<FONT color="green">140</FONT>        /**<a name="line.140"></a>
<FONT color="green">141</FONT>         * Increment the covariance matrix with one row of data.<a name="line.141"></a>
<FONT color="green">142</FONT>         *<a name="line.142"></a>
<FONT color="green">143</FONT>         * @param data array representing one row of data.<a name="line.143"></a>
<FONT color="green">144</FONT>         * @throws DimensionMismatchException if the length of &lt;code&gt;rowData&lt;/code&gt;<a name="line.144"></a>
<FONT color="green">145</FONT>         * does not match with the covariance matrix<a name="line.145"></a>
<FONT color="green">146</FONT>         */<a name="line.146"></a>
<FONT color="green">147</FONT>        public void increment(final double[] data)<a name="line.147"></a>
<FONT color="green">148</FONT>            throws DimensionMismatchException {<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>            int length = data.length;<a name="line.150"></a>
<FONT color="green">151</FONT>            if (length != dimension) {<a name="line.151"></a>
<FONT color="green">152</FONT>                throw new DimensionMismatchException(length, dimension);<a name="line.152"></a>
<FONT color="green">153</FONT>            }<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>            // only update the upper triangular part of the covariance matrix<a name="line.155"></a>
<FONT color="green">156</FONT>            // as only these parts are actually stored<a name="line.156"></a>
<FONT color="green">157</FONT>            for (int i = 0; i &lt; length; i++){<a name="line.157"></a>
<FONT color="green">158</FONT>                for (int j = i; j &lt; length; j++){<a name="line.158"></a>
<FONT color="green">159</FONT>                    getElement(i, j).increment(data[i], data[j]);<a name="line.159"></a>
<FONT color="green">160</FONT>                }<a name="line.160"></a>
<FONT color="green">161</FONT>            }<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>        }<a name="line.163"></a>
<FONT color="green">164</FONT>    <a name="line.164"></a>
<FONT color="green">165</FONT>        /**<a name="line.165"></a>
<FONT color="green">166</FONT>         * {@inheritDoc}<a name="line.166"></a>
<FONT color="green">167</FONT>         * @throws NumberIsTooSmallException if the number of observations<a name="line.167"></a>
<FONT color="green">168</FONT>         * in a cell is &amp;lt; 2<a name="line.168"></a>
<FONT color="green">169</FONT>         */<a name="line.169"></a>
<FONT color="green">170</FONT>        @Override<a name="line.170"></a>
<FONT color="green">171</FONT>        public RealMatrix getCovarianceMatrix() throws NumberIsTooSmallException {<a name="line.171"></a>
<FONT color="green">172</FONT>            return MatrixUtils.createRealMatrix(getData());<a name="line.172"></a>
<FONT color="green">173</FONT>        }<a name="line.173"></a>
<FONT color="green">174</FONT>    <a name="line.174"></a>
<FONT color="green">175</FONT>        /**<a name="line.175"></a>
<FONT color="green">176</FONT>         * Return the covariance matrix as two-dimensional array.<a name="line.176"></a>
<FONT color="green">177</FONT>         *<a name="line.177"></a>
<FONT color="green">178</FONT>         * @return a two-dimensional double array of covariance values<a name="line.178"></a>
<FONT color="green">179</FONT>         * @throws NumberIsTooSmallException if the number of observations<a name="line.179"></a>
<FONT color="green">180</FONT>         * for a cell is &amp;lt; 2<a name="line.180"></a>
<FONT color="green">181</FONT>         */<a name="line.181"></a>
<FONT color="green">182</FONT>        public double[][] getData() throws NumberIsTooSmallException {<a name="line.182"></a>
<FONT color="green">183</FONT>            final double[][] data = new double[dimension][dimension];<a name="line.183"></a>
<FONT color="green">184</FONT>            for (int i = 0; i &lt; dimension; i++) {<a name="line.184"></a>
<FONT color="green">185</FONT>                for (int j = 0; j &lt; dimension; j++) {<a name="line.185"></a>
<FONT color="green">186</FONT>                    data[i][j] = getElement(i, j).getResult();<a name="line.186"></a>
<FONT color="green">187</FONT>                }<a name="line.187"></a>
<FONT color="green">188</FONT>            }<a name="line.188"></a>
<FONT color="green">189</FONT>            return data;<a name="line.189"></a>
<FONT color="green">190</FONT>        }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>        /**<a name="line.192"></a>
<FONT color="green">193</FONT>         * This {@link Covariance} method is not supported by a {@link StorelessCovariance},<a name="line.193"></a>
<FONT color="green">194</FONT>         * since the number of bivariate observations does not have to be the same for different<a name="line.194"></a>
<FONT color="green">195</FONT>         * pairs of covariates - i.e., N as defined in {@link Covariance#getN()} is undefined.<a name="line.195"></a>
<FONT color="green">196</FONT>         *<a name="line.196"></a>
<FONT color="green">197</FONT>         * @return nothing as this implementation always throws a<a name="line.197"></a>
<FONT color="green">198</FONT>         * {@link MathUnsupportedOperationException}<a name="line.198"></a>
<FONT color="green">199</FONT>         * @throws MathUnsupportedOperationException in all cases<a name="line.199"></a>
<FONT color="green">200</FONT>         */<a name="line.200"></a>
<FONT color="green">201</FONT>        @Override<a name="line.201"></a>
<FONT color="green">202</FONT>        public int getN()<a name="line.202"></a>
<FONT color="green">203</FONT>            throws MathUnsupportedOperationException {<a name="line.203"></a>
<FONT color="green">204</FONT>            throw new MathUnsupportedOperationException();<a name="line.204"></a>
<FONT color="green">205</FONT>        }<a name="line.205"></a>
<FONT color="green">206</FONT>    }<a name="line.206"></a>




























































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